Inference for Noisy Long Run Component Process

This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out in Fama-French (1988). Moreover in the presence of a long run component, spurious regressions arise and misleading long run predictions are obtained when standard statistical approaches are applied